Question 135569
(4X^2-8X)+(Y^2+6Y)=3
4(X^2-2X+1)+(Y^2+6Y+9)=3+4+9
4(X-1)^2+(Y+3)^2=16 

{{{(X-1)^2+(Y+3)^2=4}}}

That is i the form of a circle with radius 4, centered at (1,-3)